the welfare effects of switching from consumption taxation...
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Iranian Journal of Economic Studies
Vol. 4, No. 2, Fall 2015, 1-15
The Welfare Effects of Switching from Consumption Taxation to
Inflation Taxation in Iran’s Economy
Hojjat Izadkhasti
Faculty of Economics and Political
Sciences, Shahid Beheshti University
Iran
Rahim Dallali Isfahani
Faculty of Administrative Sciences
and Economics, University of Isfahan,
Iran
Saeed Samadi
Faculty of Administrative Sciences and Economics
University of Isfahan, Iran
Abstract The net effects of switching from consumption taxation to inflation taxation on
resource allocation and welfare crucially depend on production externalities.
With elastic labor supply, raising inflation taxation decreases leisure, but
increases the levels of real consumption, capital, and output. Moreover, this tax
switch has two opposing effects on the level of real money balances: A positive
effect through the rise in output caused by the faster nominal money growth and
a negative one through the fall in the ratio of real money balances to output. In
the absence of any production, externality the negative effect dominates the
positive effect. The real effect of this tax switching on resource allocation
depends on the behavior of labor supply. If there is not a trade-off between
leisure and labor supply, then the real effect of switching to inflaction taxation
on real consumption, capital and output would disappear. With elasticity of
labor supply, the welfare effect of this tax switch is conditional on the
production externality. In the absence of production externality, inflation
taxation always reduces welfare. With a strong enough production externality,
switching from consumption taxation to inflation taxation may raise welfare by
correcting the under-investment of capital and the under-supply of labor.
Keywords: Inflation Taxation, Consumption Taxation, Welfare, Externality,
Leisure, Iran.
JEL Classifications: E40, D60.
Received: 15/2/2014 Accepted: 21/9/2016
* The Corresponding Author
Iranian Journal of Economic Studies, 4(2), Fall 2015 2
1. Introduction
Government finances can expend with nominal money growth and tax
consumption. Individuals allocate income to consumption and
investment in both capital and real money balances, and allocate time
to labor and leisure. In this environment, switching from consumption
taxation to inflation taxation drives up the cost of holding money, and
thus reduces the demand for real money balances relative to income as
is mentioned in the literature.
Further, the decrease in real money balances reduces the marginal
benefits of consumption and leisure with a non-separable utility
function concerning these augments, which tends to reduce
consumption and leisure and accordingly labor increase. The
increased labor in turn raises the marginal product of capital and
stimulates capital accumulation, leading to higher output per capita.
In the budget balances of the government, switching from
consumption taxation to inflation taxation, declines consumption tax,
tending to raise consumption. Given the standard constant elasticity of
inter temporal substitution form of the utility function in the literature
on economic growth, the net effect on the ratio of consumption to
output is zero. Thus, as output rises with the nominal money growth
rate, so does consumption. The increase in consumption tends to raise
welfare but the decline in leisure tends to reduce the welfare. The net
effects of the tax switch on real money balances and welfare depend
crucially on production externalities (Ho et al., 2007). If labor supply
were fully inelastic in our model, then switching from consumption
taxation to inflation taxation would have no real effect on real
consumption, capital and production in the long-run.
Since the positive effect of the switch to inflation taxation on
output takes time to reach its full potential through promoting capital
accumulation, the relative strength of the positive welfare effect also
depends on the elasticity of inter temporal substitution. More elastic
inter temporal substitution accelerates growth and hence strengthens
the positive welfare effect. The net welfare effect of switching from
consumption taxation to inflation taxation can be positive so long as
the externality is strong enough. However, when considering the
entire equilibrium path in a tractable AK model with a strong enough
The Welfare Effects of Switching from Consumption Taxation to … 3
externality for endogenous growth, a positive net welfare effect of this
tax switch also requires the elasticity of inter temporal substitution to
be sufficiently high. By reducing the consumption tax and raising the
inflation tax to finance, a given government fiscal commitment can
stimulate production in the long-run in our model, as opposed to the
long-run neutrality of money growth in Rebelo and Xie (1999)
without a consumption tax.
The paper is organized as follows: Section 2 reviews the related
studies in the field. Section 3 introduces the model. Section 4,
Maximizes welfare function in steady state. Empirical results are
present in Section 5 and the last section concludes.
2. Literature Review
When money enters directly in to the utility function and interacts
with an elastic labor, money is generally non-supernatural (Brock,
1974; and Ho et al., 2007). If money and capital were substitute,
higher monetary growth enhances capital accumulation (Tobin, 1965).
In the case, money is required for purchasing capital goods, higher
anticipated inflation decreases steady-state real balances and capital
stock, and hence a reversed Tobin effect emerges (Stockman, 1981;
Lu et al., 2011).
Some studies support a rate of money growth for a positive
nominal interest rate by considering additional factors such as
production externality, elastic labor supply, and distortion of other
taxes on labor, output, and consumption. In Phelps (1973), Braun
(1994), and Palivos and Yip (1995), inflation taxation leads to a
higher welfare than income taxation as a means of public finance1. In
Rebelo and Xie (1999), money does not affect production in the
steady state, but can alter it during the transition toward the steady
state; and the transitional effect be exploited by monetary policy to
improve welfare, if there are production externalities.
Ho et al. (2007) offered a comparison of the welfare cost between a
seignorage tax and a consumption tax in the public finance approach
in a model with real balances and leisure in utility. They found that
without a production externality, a seignorage tax always had a higher
welfare cost than a consumption tax in the long- run. With a
Iranian Journal of Economic Studies, 4(2), Fall 2015 4
production externality, a seignorage tax not only had a smaller welfare
cost than a consumption tax but may have a welfare gain.
Lu et al. (2010), investigates welfare costs between seignorage and
consumption taxes in a neoclassical growth model with a cash-in-
advance constraint. They compares equilibrium along transitional
dynamic and steady-state paths and finds that because of lower
consumption and leisure and thus higher welfare costs of consumption
taxes during early periods, the welfare cost of consumption taxes is
larger than the welfare cost of seignorage taxes.
Izadkhasti et al. (2015) from sensitivity analysis in a steady state
found that without externality of production, by increasing inflation
tax rate, the ratio of consumption to GDP remains constant, but labor,
capital stock and production will increase. With decrease in the ratio
of real money balances to GDP and leisure, the level of social welfare
in steady state decreases. Considering production externality, capital
stock and a rapid production increase, welfare level increases in
steady state.
3. The Basic Model
The problem of determining the optimal structure of taxes to finance a
given level of expenditures is called the Ramsey problem, after the
classic treatment of Ramsey (1928). In the representative-agent
models we have been using, the Ramsey problem involves setting
taxes to maximize the utility of the representative agent, subject to the
government’s revenue requirement.
3-1. Household
the economy is populated by infinite families whose wealth is in the
form of either money or capital. Each household solves the following
maximization problem:
0
max (c ,m ,l )exp[ t]dt, u , 0, , 0t t t c m cc mmW u u u u
(1)
. : 1 1t t tt t t t c t m t
da dk dms t w l r k c m
dt dt dt
(2)
The Welfare Effects of Switching from Consumption Taxation to … 5
Where,c , m and tl are real consumption, real money balances, and
leisure respectively. ρ is the constant rate of time preference. tk is the
capital stock, m is a rate of inflation tax, and is a rate of
consumption tax. Assume that the rate of population growth is zero.
The transversality condition ruling out the Ponzi game is given as: ρt
tlime 0t ta
(3)
3-2. Firms
Firms produced a final good by using capital , and labor ,
according to the following technology: 1
tY A(1 ) 0 1,0 1t t tKl K (4)
Where is the final output, is total factor productivity, and
measures the importance of capital relative to labor in production.
Average capital ̅ exhibits spillovers of degree . Marginal product of
factors are:
α α
t t tA 1 α K (1 l )w
(5) α 1 1 α
t tAαK (1 l )tr
(6)
Where is the real wage rate and is the real interest rate.
3-3. Government
Assume that government uses a consumption tax and inflation tax to
finance consumption expenditure and uses others revenue to
finance capital expenditure , Denoting
t tt co caG G G . Assume
that consumption government spending is a fixed fraction , of final
output with . Suppose that the consumption government budget
is balance at each point in time:
c t m cot t tc G βf k ,1 l ,β 0tm
(7)
4. Maximizing Welfare Function in Steady-State
By considering the utility function by:
Iranian Journal of Economic Studies, 4(2), Fall 2015 6
1
0
exp( t)1
t t tc m lW dt
(8)
Where δ, θ, and η measure the importance of real consumption,
real money balances, and leisure, respectively, and ⁄ is the
elasticity of intertemporal substitution. The steady-state welfare
function obtained as follows (Izadkhasti et al., 2015):
1
ss Ф[F( , )]
1
c mW
(9)
Where
(δ θ)
δ η δ 1 α
1 α η
1 α
(ρ ) (1 ) [δ ρ θ ]F ,
{η ρ (1 α)[δ ρ θ ]}
m c m m
c m
m m m
and
η 1 111{ η [ (1 ) ( ) ] } 0Ф A
The steady-state welfare level , is a function of the rates of
consumption tax and inflation tax. is a constant and
independent of the consumption tax and inflation tax. The steady-state
welfare level is monotonically increasing with . We focused on in
the welfare analysis with or without the production externality.
With respect to equation (7), Izadkhasti et al. (2015), obtained
consumption-output ratio and real money balances- output ratio in the
steady-state:
θ
1 θ θ
c m m
c m m m m
(10)
In the absence of any production externality ( 0) , the steady-
state welfare level in equation (8), reduces to:
δ η δ(ρ ) (1 )F ,
η ρ (1 α)[δ ρ θ ]
ss ssss ss m cc m ss ss ss
m m m
(11)
In the case with consumption taxation only, from equation (10), we
The Welfare Effects of Switching from Consumption Taxation to … 7
have /1 βss
c , and:
θ δ
0 (ρ) (1 β)F
η (1 α)δ
ss
c
(12)
Where the assumption θ has been used to simplify the
expression. In the case with inflation taxation only, from equation
(10), we have δρ / θ 1 β βδss
m , and:
θ δ η θ
0(ρθ) (1 β) [θ 1 β βδ]
Fη (1 α)δ
ss
m
(13)
By comparing the two regimes in the steady-state without any
production externality and with 𝛽 and 𝛽 𝛽 ⁄ , shows
that using consumption taxation to finance government spending
obtains a higher welfare level than using pure inflation taxation.
Without any production externality, we have:
( )( )
( ) (1 ) [ 1 ]
ss
c
ss
m
F
F
(14)
Obviously, at 𝛽 we have , and for 𝛽 we have
1 . In the steady-state without any production externality and with
> 0, if both consumption taxation and inflation taxation are used to
finance government spending, government maximizing welfare
function ,( )sss
c
s
mF in equation (8), subject to its budget constraint
(10). Lagrangian function is as follows:
F , μ{ β}
1
ss ssmss m
m ss ssss ssm mm
css
c s
m
s
c
L
(15)
Where, µ is the multiplier. The first-order condition with respect to ss
c is:
2
F , ( )0
1 (1 ) [ ]
ss ss ssc m m
ss ss ss ss ssc c c m m
L
(16)
The first-order condition with respect to ss
m , we get:
Iranian Journal of Economic Studies, 4(2), Fall 2015 8
2
F , [η ( )(1 )] F , ( η)
η 1 [ ]
(1 )
ss ss ss ss
c m c m
ss ssss ss ssm mm m m
ss ss ss
m m c
L
(17)
With any production externality, if 0ss
mL , it is convenient to
start with consumption taxation ss
c (1 ) and 0ss
m . Starting
with consumption taxation we have
F , μ (1 β) δ, F , 0ss ss ss ss
c m c m . If 0ss
mL at
ss
c (1 ) and 0ss
m , then there should be deflation 0ss
m
and accordingly ss
c (1 ) . Using
F , μ (1 β) δ, F , 0ss ss ss ss
c m c m in equation (16) and
rearranging terms, we have:
ss
c
β1 0 0
1 β
ss
mss
m
Lsign sign at and
(18)
In the steady-state without any externality and with , if both
consumption taxation and inflation taxation are used to finance
government spending, their optimal mix to maximize welfare, the rate
of the inflation tax should be negative and the rate of consumption tax
should be positive. The intuition is as follows: Since real money
balances and consumption enter the utility symmetrically, there is a
uniform taxation principle saying that the government should tax both
at the same rate in order to avoid distorting the margin between
consumption and real money balances2. This consideration implies
that the rates of consumption and inflation taxes should be equal.
However, real money balances are also an asset and ideally, the
government does not want to distort the return on money relative to
the return on capital to avoid distorting the margin between real
money balances and capital. Since capital income is not taxed in our
model, this consideration implies that the inflation tax should be zero.
Combining the consumption-money consideration with the capital-
The Welfare Effects of Switching from Consumption Taxation to … 9
money consideration suggests that, in the absence of any externality,
the consumption tax should exceed the inflation tax. Moreover, in the
spirit of the Friedman rule, because the social cost of producing
money is zero, there should be a negative inflation tax such that the
cost of holding money can be as close to zero as possible. As a result,
the optimal inflation tax is negative along with a positive consumption
tax. However, the underlying nominal money growth rate should
exceed the rate that corresponds strictly to the Friedman rule, because
of the distortions of the consumption tax and the negative inflation tax
on leisure and consumption.
In the steady-state with production externality and with > 0, if
both consumption taxation and inflation taxation are used to finance
government spending, government maximizing welfare function
,( )sss
c
s
mF in equation (8), subject to its budget constraint (10).
Lagrangian function is as follows:
F , μ{ β}
1
ss ss ssc mss ss m
c m ss ssss ss ssm mc m m
L
(19)
Differentiating the Lagrangian with respect to ss
m , we have:
2
2
F , (1 η )[η ( )(1 )] F , ( η)
(1 ){η 1 }
F , ( θ)
(1 ) (1 )
ss ss ss ss
c m c m
ss ssss ss ss
m mm m m
ss ss
c m
ss ss ss ss ssm m m m c
L
(20)
Using F , μ (1 β) δ, F , 0ss ss ss ss
c m c m in this equation and
rearranging terms, we have:
ss
c
(1 ) [ (1 )] 1 (1 )
β 0
1 β
ss
m
ss
m
Lsign sign
at and
(21)
Note that ss
mL is increasing in ψ. If ψ approaches (1 ) , then:
Iranian Journal of Economic Studies, 4(2), Fall 2015 10
{ η 1 α 1 η } 0ss
m
Lsign sign
(22)
In the steady-state with > 0, when consumption taxation is used
to finance government spending, inflation taxation should also be used
together if ψ ∈ (0, 1 − α) is large enough. If 0ss
mL at ss
c (1 ) and 0ss
m then ss π 0ss
m .
With a weak production externality 0,1 , we are able to
compare inflation taxation with consumption taxation. Using
consumption taxation to finance government spending means
/ (1 )ss
c and 0ss
m . Substituting these into the definition of
F , c m we have:
(δ θ)
θ δ 1 α
1 α η
1 α
ρ (1 β) δF
[η 1 α δ]
ss
c
(23)
Similarly, with inflation taxation βδρ / θ 1 β βδss
m and
0ss
c , we have
ψ(δ θ)
1 α ψ
ψ(δ θ)
θ δ η θ 1 α ψ
δ
(ρθ) (1 β) [θ 1 β βδ] δF
[η(1 β) (1 α)δ]
ss
m
(24)
In the steady-state with 𝛽 , and δ / 1 , if
0,1 is large enough, then using inflation taxation to finance
government spending obtains a higher welfare level than using
consumption taxation. The ratio of the two welfare levels is defined
as:
1 α ηψ
η θ 1 α ψF θ η(1 β) δ(1 α))
(1 β) [ ] [ ] H(β)θ 1 β βδ η δ(1 α)F
ss
c
ss
m
(25)
Here, it is obvious that , for ,θ(1- ) and for a
The Welfare Effects of Switching from Consumption Taxation to … 11
large enough we have .
When there is a production externality, the private rate of return on
investment in capital is lower than the social rate, leading to under-
investment in capital. When the level of capital is below its socially
optimal level, the private rate of return on labor must also be lower
than the social rate, leading to a suboptimal solution with too little
labor and much leisure. There for, the positive effects of inflation tax
on labor and capital accumulation can increase the output. The rise in
the inflation tax raises real consumption in the steady state3. With a
strong enough externality, the rise in the inflation tax may raise real
money balances in the steady state, rather than reduces it as in without
production externality case4. Thus, the rise in the inflation tax can
improve welfare level in the steady state when the production
externality is strong enough for the welfare gain from increasing
consumption and possibly real money balances dominate the welfare
loss by decreasing leisure.
5. Empirical Results
Using numerical solution based on the parameterization ,
, , , , η and δ in Iran’s
Economy, the quantitative implications of the results are illustrated in
Tables 1. We first selected a benchmark case and made a steady-state
welfare comparison with and without production externality.
Iranian Journal of Economic Studies, 4(2), Fall 2015 12
Table 1. Numerical Results in the Steady State With and Without
Production Externality ( 0.50)
Cases % m % c
ssc ssl ssm ssk ssy ssW
Benchmark 0.00 0.00 0.00 0.934 0.417 1.56 2.80 0.934 58.56
Wit
hou
t ex
tern
alit
y 0.23 -3.00 39.86 0.697 0.435 2.32 2.71 0.905 55.07
0.23 -2.00 35.52 0.706 0.427 1.99 2.75 0.917 54.73
0.23 -1.00 32.32 0.714 0.421 1.75 2.78 0.927 54.42
0.23 0.00 29.87 0.719 0.417 1.56 2.80 0.934 54.14
0.23 2.00 26.36 0.727 0.410 1.28 2.83 0.945 53.66
0.23 4.00 23.97 0.733 0.405 1.08 2.86 0.952 53.26
0.23 6.00 22.23 0.737 0.402 0.939 2.87 0.958 52.90
0.23 23.43 0.00 0.752 0.390 0.959 2.93 0.977 53.03
Wit
h w
eak
exte
rnal
ity
0.00 0.00 0.00 12.28 0.417 20.47 36.84 12.28 144.3
0.23 0.00 29.87 42.77 0.417 92.57 36.84 55.54 226.2
0.23 2.00 26.36 43.11 0.410 75.66 38.33 55.98 223.9
0.23 4.00 23.97 43.34 0.405 63.97 39.39 56.29 222.1
0.23 6.00 22.23 43.52 0.402 55.41 40.18 56.52 220.5
Source: Researchers Computations
In the Table 1, we assume that no government intervention happens
in the first case in the benchmark. In the second case, either or both of
consumption taxation and inflation taxation be used to finance
government current expenditure as 23% of output (𝛽 )5. When
both instruments are used6, without production externality their
optimal mix is a positive consumption tax and a negative inflation tax
(a deflation transfer at a rate of nominal money growth -3.0%),
implying higher real money balances than in the benchmark.
Compared to the both instruments are used regarding real allocation
and welfare, this optimal mix has higher leisure but lower levels of
real consumption, capital, output and welfare in the steady-state than
in the benchmark.
When the consumption tax is used alone to finance government
spending, there is no real effect on the allocation of time and output.
Since government spending is wasted, the consumption tax reduces
the welfare. When the inflation tax is used alone in the steady-state,
there is a greater loss in the welfare compared to the no intervention
case because the inflation tax (at a 23.43%) reduces consumption,
The Welfare Effects of Switching from Consumption Taxation to … 13
leisure and real money balances compared to the no-intervention case.
In this case, there is a greater loss in the welfare.
6. Conclusion
This paper considered the effects of switching from consumption
taxation to inflation taxation on resource allocation and welfare.
Concerning resource allocation, we found that switch to inflation
taxation decreases leisure and real money balances, but increases the
levels of consumption, capital, and output. The welfare effect of
inflation taxation is conditional on the strength of production
externality and on the elasticity of labor supply. In the absence of
production externality, switch to inflation taxation always reduces the
welfare, whether it used alone or with consumption taxation. In
essence, as the rate of inflation taxation rises along with a falling
consumption tax rate, the losses in welfare arising from the decreases
in leisure and real money balances dominate the gain from the
increase in consumption.
With a strong production externality, the positive output effect of
the increasing from switch to inflation taxation may lead to a positive
net effect on the level of real money balances. The effects of
switching from consumption taxation to inflation taxation may raise
welfare by correcting the under investment of capital and the under-
supply of labor.
Endnotes
1-Phelps (1973), Braun (1994), and Palivos and Yip (1995), assume
that the government finances spending by an income tax and
inflation tax.
2- See Atkinson and Stiglitz (1972) for more discussions on the
uniform taxation principle.
3- ss ss
cΓ Yssc
4- ss ss
mΓ Yssm
5- Is according to central bank statistics of Iran.
6- However, the underlying inflation tax rate should exceed the rate
that corresponds strictly to the Friedman rule, because of the
Iranian Journal of Economic Studies, 4(2), Fall 2015 14
distortions of the consumption tax and the negative inflation tax on
leisure and consumption.
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